To earn this trophy, you need to kill 25 enemies with pistols. Any pistol-like secondary weapon will count for this, including: revolvers, burst, semiauto, and auto pistols. And, while not necessary, I would highly recommend using a semiauto pistol, aiming down the sights, and lining up easy headshots towards:
There is no in game tracker for pistol kills. Instead, just reach an area on the map where several waves of enemies come pouring in. I suggest using a semiauto pistol, and aiming down the sights.
If you don't reach your 75 kills during your run, just kill every enemy in an area, until only one is left, then either let him kill you to reset the checkpoint, or kill him and pause to reset the checkpoint. Repeat until the trophy pops. (Restarting checkpoint does not lose track of progress).
Please vote if you found this helpful, and comment if you have any additional insight or questions. Feel free to add me on TT, TA, PSN, or XBL, username: Danokitty.
Happy hunting!
-Dan